Quantum Mechanics Solution Manual 

© Leon van Dommelen 

2.5.1 Solution eigvalsa
Question:
Show that , above, is also an eigenfunction of , but with eigenvalue . In fact, it is easy to see that the square of any operator has the same eigenfunctions, but with the square eigenvalues.
Answer:
Differentiate the exponential twice, [1, p. 60]:
So turns into ; the eigenvalue is therefore which equals .